A Short Count

“Innumeracy: Mathematical Illiteracy And Its Consequences” (1988©) — book review
Today’s book review is for: “Innumeracy: Mathematical Illiteracy And Its Consequences“, written by John Allen Paulos.  The book is an overview of what the author believes are some of the symptoms (and solutions) of “innumeracy” (the math equivalent of illiteracy) in America.  Paulos is a Professor of maths at Temple University (or was at the time of the publication).  He is a bit of a math prodigy (at the very least precocious) and is kind of a cross between Richard Feynman, Malcolm Gladwell and Levitt & Dubner.  Feynman – as a teacher – in converting technical (math) concepts into relatable images, Gladwell in writing for “the general public” consumption, and Levitt & Dubner (of “Freakonomics” fame) in both of the above plus quirky examples to illustrate his point.
This book is a quick (fast read) and short (135 pages) overview of some main concepts in math and how they are poorly taught / translated / communicated to the general public and, hence, the general distaste for maths during school and its avoidance post-formal education whenever possible.
Paulos’ proposition is that because maths are poorly taught, the general public grows up with a fear (and avoidance) of math for the rest of lives.  One of his proposals is to take retired advanced math users (mathematicians, engineers, scientists) and have them teach in schools because the current maths teachers aren’t very good (for a number of reasons) – pun intended.
The author also reviews math concepts: scale (big and little), fractions, ratios, statistics, probabilities and pseudo-sciences.  This overview / review is the strength of the book as it reminded me of many of the areas of math I’ve long since forgotten (for lack of use).
So, is this book any good?  Does it make you feel numerate or innumerate?  Does it help with the issue raised (innumeracy)?  Yes.  Both.  And, no, or at least I don’t think so.  Once I could get past the author’s ego / superiority complex, I actually quite enjoyed the book.  It is a fast read and he does use his examples in a clear and sometimes humorous fashion.  The text made me feel numerate.  The work through examples innumerate.  A few of the paragraphs had to be re-read to make sure I followed the explanations for why he was doing a particular calculation.  For example, how many days is a million seconds?  The author says eleven-ish.  So, then how long is a billion seconds?  Again, thirty something years.  Now, the author actually worked out the numbers and provided the answers.  The problem?  Well, for me, the answer is 11(-ish) thousand days.  I would never arbitrarily convert days to years.  Not that I couldn’t; just that I wouldn’t.  Why would I, unless specifically asked?  And, for most purposes, I would have ball-parked it (1,000 days is almost 3 years, times 11 is “about” 33 years).  It would not be entirely accurate, but even then, the author didn’t state he was accounting for leap years in his own calculations.  His point was we “all” know how much a second is.  What we don’t know (have a feeling for) is how big a number is a billion (or a million).  My point is I’m not sure if my reaction means I’m personally numerate or innumerate.  And, finally, simply pointing out a problem isn’t the same as offering a viable solution.  I don’t think placing retired math users in schools is a workable solution.  Teaching (across all of the non-adult years) is an art as much as it is a skill.  Yes, you must be grounded in the material, but you must also be enthusiastic (about the subject and teaching) and relatable.  I’m not convinced there is a vast pool of retired engineers and scientists just dying to teach grammar, middle and high school students (and each group has different requirements).
Final recommendation:  Strong to highly recommended.  As an overview of maths topics for the general public, I think this is a very valuable book.  It is brief and has interesting examples.  It is probably too simple for folks with college level math skills.  It is probably too difficult for the truly innumerate.  But, I think there is a wide, flat(ish) bell shaped curve of folks out there (probably 2 standard deviations on either side of the mean) who would gain from reading this book.  Those below the mean because the writing and examples are clear and can be followed along with.  Those above the curve, because the book will remind you how much you’ve forgotten since leaving school.  I just wish the author had been a bit less patronizing of us non-math prodigies.
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Accustomed To It

“I wish to become a teacher of the Truth.”
“Are you prepared to be ridiculed, ignored and starving till you are forty-five?”
“I am. But tell me: What will happen after I am forty-five?”
“You will have grown accustomed to it.”
—   Anthony De Mello
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Gratitude And Warmth

One looks back with appreciation to the brilliant teachers, but with gratitude to those who touched our human feelings.  The curriculum is so much necessary raw material, but warmth is the vital element for the growing plant and for the soul of the child.
—  Carl Gustav Jung
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2017	Never Forget
2016	It’s All Greek To Me (Well, Latin Actually)
2015	Truism
2014	Thank You
2013	Really
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2011	The Wealth Of Sons (And Daughters)

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Shedding Light

If a man is to shed the light of the sun upon other men, he must first of all have it within himself.
—   Romain Rolland
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Reinforced Learning

To teach is to learn twice.
—  Joseph Joubert
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Nothing Is Known Absolutely

Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show.
—  Richard P. Feynman
Quoted by James Gleick, in his book: “Genius“
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Nurture Tolerance

…What drove me to teach were two sparks.  The spark in a student’s eye when they grasped their way with confidence; and the spark in my eye when a student revealed a different perspective to mine.  That’s why I loved being an English teacher.  It was all about sharing different interpretations, perspectives and nuances that lay within a landscape of words speaking truths only made real in someone else’s mind.  My role was to enable that thought freedom and to nurture tolerance.  My job was to allow people unique views in on the worlds we studied each day and for my eyes to be widened by their perspective.  Learning happened all round and, if I ever did my job right, on all levels too.
—  From a blog I follow: “The Bamboo Principle“, located at: http://thebambooprinciple.wordpress.com/
The specific post was: http://thebambooprinciple.wordpress.com/2013/10/08/a-job-of-it/
[Another great blog to check out if you haven’t already…  And, yes, back in 2010, I still didn’t know about scheduling posts.  In a way, it’s nice to be reminded we’re all beginners at some point.  —  KMAB]
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What Is Your Canvas?

Looking back, perhaps the lesson I would draw is this: If you don’t love it, don’t do it.  I loved it — teaching people how to reach in deep to fulfill their potential, how to become great.  And when you do that with a group, you, as the leader, enjoy the thrill of creating a great team.  For me it was like creating a work of art.  Only instead of painting on a canvas, I had the great joy of creating in collaboration with others.
—  Bill Walsh
From his book: “The Score Takes Care Of Itself“
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